1. Relations and Functions
Standard: M8A3 c. Distinguish
between relations that are functions and those that are not functions.

2. Relation = { (3,5),(-2,8),(-3,8),(0,-6) }
A ________ is a set of __________________.
relation
ordered pairs
Relation = { (3,5),(-2,8),(-3,8),(0,-6) }
The ________ is the ______ of ______ values.
domain
set x
The ________ is the ______ of ______ values.
range
set y

3. Domain: { ____, ____, ___, ____}
EXAMPLE
Relation = { (3,5),(-2,8),(-3,8),(0,-6) }
Domain: { ____, ____, ___, ____}
Range: {____ , ___, ____}

4. Domain: { ____, ____, ___, ____} -3 -2 3
EXAMPLE
Relation = { (3,5),(-2,8),(-3,8),(0,-6) }
Domain: { ____, ____, ___, ____} -3 -2 3
Range: {____ , ___, ____}

5. Domain: { ____, ____, ___, ____} -3 -2 3
EXAMPLE
Relation = { (3,5),(-2,8),(-3,8),(0,-6) }
Domain: { ____, ____, ___, ____} -3 -2 3
Range: {____ , ___, ____} -6 5 8

6. -3 -2 3 -6 5 8 Domain Range Three other ways to represent a relation:3 -6 5 8
1. Mapping:

7. x y -3 -2 3 8 -6 5 Three other ways to represent a relation: 2. Table:
domain
range x y -3 -2 3 8 -6 5

8. Three other ways to represent a relation:
3. Graph:

9. Example 1: Represent the following relations as a set of ordered pairs.-2 5 6 -3 2 7
{ }
(-2, 2)
(0, -3)
(5, 7)
(6, 7)

10. { }
(2,0)
(-2,2)
(-2,-2)
(-6, 2)

11. y x -3 -1 2 4 -2 3 -7 4
{ }
(-3,0)
(-1,-2)
(0,3)
(2,-7)
(4,4)

12. Functions can be represented four different ways:
A ___________ is a relation in which no number in the
_________ is __________. (the x-value can not
repeat)
function
domain
repeated
Functions can be represented four different ways:
1. ______________
2. ______________
3. ______________
4. ______________
mapping
graph
table
set of ordered pairs

13. Example 2: Represent the following function as a mapping, graph, and table.
{(7,4),(-3,6),(5,8),(4,3),(1,-3)} -3 3 4 6 8 -3 1 4 5 7

14. {(7,4),(-3,6),(5,8),(4,3),(1,-3)}

15. {(7,4),(-3,6),(5,8),(4,3),(1,-3)} y x -3 6 1 -3 4 3 5 8 7 4

16. Each element of the domain is only used once.
Example 3: Are the following relations also functions? -2 3 -7 -2 3 -7 -4 5 8 -4 5 8
Each element of the domain is only used once.
3 is used twice.
NOT A
FUNCTION
FUNCTION

17. Will all vertical lines cross the graph at only one point?
FUNCTION
Will all vertical lines cross the graph at only one point?
YES. Each x is only used once.

18. Will all vertical lines cross the graph at only one point?D
FUNCTION
Will all vertical lines cross the graph at only one point?
YES. Each x is only used once.

19. Will all vertical lines cross the graph at only one point?
NOT A
FUNCTION
Will all vertical lines cross the graph at only one point?
NO. x =-3 is used twice.

20. Will all vertical lines cross the graph at only one point?F
NOT A
FUNCTION
Will all vertical lines cross the graph at only one point?
NO. x =-2 is used three times.

21. Are all x values used only once?-4 -2 2 -3 3 1
NOT A
FUNCTION
Are all x values used only once?
NO. x = - 4 is used twice.